A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of Non-Standard Discretisation Methods, Mechanical and Mathematical Analysis’. © 2020, The Author(s)

The Finite Cell Method for Simulation of Additive Manufacturing

Additive manufacturing processes are driven by moving laser-induced thermal sources which induce strong heat fluxes and fronts of phase change coupled to mechanical fields. Their numerical simulation poses several challenges, e.g. the evolution of the (possibly complex) domain as the specimen is produced and the differences in scales of the problem. In this work, the first aspect is addressed using the Finite Cell Method, an immersed approach that removes the need for meshing and is able to accurately handle complex geometries. For the second aspect we develop a framework with local refinement to selectively increase accuracy where needed, and derefinement in previously refined regions far from the laser source to keep the overall computational cost constant throughout the simulation. In this work, we present the essential theoretical fundament of the computational framework. Then, we show its application to model additive manufacturing processes in various examples, including experimental validation

Hierarchically refined isogeometric analysis of trimmed shells

This work focuses on the study of several computational challenges arising when trimmed surfaces are directly employed for the isogeometric analysis of Kirchhoff–Love shells. To cope with these issues and to resolve mechanical and/or geometrical features of interest, we exploit the local refinement capabilities of hierarchical B-splines. In particular, we show numerically that local refinement is suited to effectively impose Dirichlet-type boundary conditions in a weak sense, where this easily allows to overcome the issue of over-constraining of trimmed elements. Moreover, we highlight how refinement can alleviate the spurious coupling stemming from disjoint supports of basis functions in the presence of “small” trimmed geometrical features such as thin holes. These phenomena are particularly pronounced in surface models defined by complex trimming patterns and with details at different scales. In this contribution we focus our effort on the analysis of single-patch geometries, where we show through several numerical examples the benefits and computational efficiency of the proposed methodology

Ricentrare la città: paesaggi culturali nella metropoli contemporanea

Questo volume, come ricorda Cristina Messa nell’introduzione, si presenta come uno strumento utile per arricchire le conoscenze sul Distretto Bicocca, rete di eccellenza che, da settembre 2016, ha iniziato ad operare attivamente e vuole essere un punto di riferimento per i cittadini e gli operatori (enti, fondazioni, aziende e comuni) dell’area Nord della Città metropolitana di Milano. Ezio Marra analizza il dibattito scientifico e legislativo che ha portato alla costituzione delle città metropolitane. Il capitolo offre alcuni spunti di riflessione sul caso di Milano, che si sta attrezzando per diventare una Grande Milano policentrica

Biofabricated soft network composites for cartilage tissue engineering

Articular cartilage from a material science point of view is a soft network composite that plays a critical role in load-bearing joints during dynamic loading. Its composite structure, consisting of a collagen fiber network and a hydrated proteoglycan matrix, gives rise to the complex mechanical properties of the tissue including viscoelasticity and stress relaxation. Melt electrospinning writing allows the design and fabrication of medical grade polycaprolactone (mPCL) fibrous networks for the reinforcement of soft hydrogel matrices for cartilage tissue engineering. However, these fiber-reinforced constructs underperformed under dynamic and prolonged loading conditions, suggesting that more targeted design approaches and material selection are required to fully exploit the potential of fibers as reinforcing agents for cartilage tissue engineering. In the present study, we emulated the proteoglycan matrix of articular cartilage by using highly negatively charged star-shaped poly(ethylene glycol)/heparin hydrogel (sPEG/Hep) as the soft matrix. These soft hydrogels combined with mPCL melt electrospun fibrous networks exhibited mechanical anisotropy, nonlinearity, viscoelasticity and morphology analogous to those of their native counterpart, and provided a suitable microenvironment for in vitro human chondrocyte culture and neocartilage formation. In addition, a numerical model using the p-version of the finite element method (p-FEM) was developed in order to gain further insights into the deformation mechanisms of the constructs in silico, as well as to predict compressive moduli. To our knowledge, this is the first study presenting cartilage tissue-engineered constructs that capture the overall transient, equilibrium and dynamic biomechanical properties of human articular cartilage

A Selection of Benchmark Problems in Solid Mechanics and Applied Mathematics

In this contribution we provide benchmark problems in the field of computational solid mechanics. In detail, we address classical fields as elasticity, incompressibility, material interfaces, thin structures and plasticity at finite deformations. For this we describe explicit setups of the benchmarks and introduce the numerical schemes. For the computations the various participating groups use different (mixed) Galerkin finite element and isogeometric analysis formulations. Some programming codes are available open-source. The output is measured in terms of carefully designed quantities of interest that allow for a comparison of other models, discretizations, and implementations. Furthermore, computational robustness is shown in terms of mesh refinement studies. This paper presents benchmarks, which were developed within the Priority Programme of the German Research Foundation ‘SPP 1748 Reliable Simulation Techniques in Solid Mechanics—Development of NonStandard Discretisation Methods, Mechanical and Mathematical Analysis’